Several numerical methods can be used to solve ordinary differential equations. These equations are especially useful
when differential equations cannot be solved analytically.

The general form of the first-order equations can be expressed by:

y' = f (x,y)

and the higher-order equations can be written:

y(n) = f (x, y, y', y'',..., y(n-1))

The task is to determine the necessary boundary conditions and the relationships between x and y.

A common way of handling a second- or higher-order equations is to replace it with an equivalent system
of first-order equations. The higher-order equation above can always be transformed into a set of n first
order equations. Using the notation:

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